Temperature-Robust MEMS Gyroscope with 2-DOF Sense-Mode Addressing the Tradeoff Between Bandwidth and Gain

ABSTRACT

The current invention is a novel gyroscope design, which yields devices robust to fabrication and environmental variations, allows flexible selection of operational parameters, and provides increased bandwidth with minimized sacrifice in gain regardless of the selected frequency of operation. The gyroscope has a single degree-of-freedom (DOF) drive-mode and a 2-DOF sense-mode. The drive-mode operational frequency and the sense-mode bandwidth can be selected arbitrarily in the proposed design, relaxing the tradeoff between the gain, die size, and detection capacitance. The symmetry of the structure ensures the optimal location of the drive-mode resonance relative to the sense-mode operational region, even in presence of fabrication imperfections.

RELATED APPLICATIONS

The present application is related to U.S. Provisional PatentApplication Ser. No. 61/030,522, filed on Feb. 12, 2008, which isincorporated herein by reference and to which priority is claimedpursuant to 35 USC 119.

GOVERNMENT RIGHTS

This invention is made with Government Support under Grant numberCMS0409923, awarded by the National Science Foundation. The Governmenthas certain rights in this invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to the field of micromachined virbratorygyroscopes, in particular gyroscopes with a one degree-of-freedom drivemode and a two degree-of-freedom sense mode.

2. Description of the Prior Art

The operation of all micromachined vibratory gyroscopes is based on atransfer of energy between two modes of vibration caused by the Corioliseffect. Conventional implementations often utilize single degree offreedom drive and sense-modes. Several of these conventionalimplementations reported gyroscopes with structurally symmetricaldesigns aimed at mode-matched operation. In such implementations, themechanical gain is increased proportionally to the sense-mode qualityfactor. Additionally, mode-matching feedback control can be employed toimprove sensitivity by electronically tuning the drive- and sense-modes.Alternatively, parametric excitation of the drive-mode providing largeamplitudes over a wide range of frequencies can be used to eliminate thefrequency mismatch between the drive- and sense-modes. However,mode-matched operation has practical challenges, requiring precisematching of the operational modes over wide temperature ranges. As aresult of mode-matched operation, the increased sensitivity is achievedat the cost of sensor robustness, temperature bias drift, bandwidth andlinear operational range.

Alternatively, the modes of operation can be designed with a certainfrequency mismatch. Even though this approach improves the robustnessand the bandwidth characteristics, the improvements are limited due tothe dimensionality of the design space. Restrictions of designapproaches with single-DOF drive- and sense-modes dictate a tradeoffbetween achieved robustness/bandwidth and gain.

Structural design approaches leading to robust gyroscopes are anintriguing option to consider. Several approaches have been previouslyexplored including a design of a non-resonant gyroscope with 2-DOFdrive- and 2-DOF sense-modes, and a gyroscope design with a 2-DOFdrive-mode and 1-DOF sense-mode. Previously reported designs illustratedthat the increase of system dimensionality and careful selection ofsystem parameters may lead to an increase of system robustness. However,increasing the number of degrees of freedom in the drive-mode may not bethe best choice as it requires actuation of the drive-mode at anon-resonant frequency, which is less efficient than resonant actuation.

For increasing robustness of vibratory gyroscopes, it is beneficial todesign 1-DOF drive- and 2-DOF sense-modes so that the drive-moderesonant frequency is placed between the two resonant peaks of thesense-mode. A single-DOF drive-mode is more suitable forresonance-locking closed loop operation, similar to conventionalgyroscopes. A 2-DOF sense-mode provides extended design flexibility androbustness by utilizing a dynamically coupled response when thedrive-mode is operated in between the two coupled resonant peaks. Forexample, one such design found in the prior art has been demonstrated toprovide robust operation with a 200 Hz bandwidth using a micromachinedprototype with a 750 Hz operational frequency. For this design concept,increasing the operational frequency would further increase thebandwidth, while also resulting in a decrease of the sensitivity.

Most real-world applications such as automotive, military, and consumerelectronics require robust yet sensitive gyroscopes with operationalfrequencies above several kHz in order to suppress the effect ofenvironmental vibrational noise. At the same time, the desiredmechanical bandwidth of the sense-mode is typically above 100 Hz, butnot more than 400 Hz.

Previous gyroscopes employing a 2-DOF sense-mode rely on a dynamicvibration absorber (DVA) structure, in which the frequency responsecharacteristics strongly depend on both the operational frequency andthe ratio between the smaller and the bigger sense-mode masses. In thiscase, the gain of the gyroscope is inversely proportional to the spacingbetween the sense-mode peaks. Adapting the DVA-based gyroscope designfor operational frequencies above 1 kHz while maintaining the sense-modepeaks at a practical spacing is challenging due to the limitation of thedesign space and involves a stringent tradeoff between the die size anddetection capacitance.

Therefore, a new gyroscope design concept is desired which wouldpreserve the advantages of the multi-DOF concept, while eliminating thescaling tradeoff and allowing flexible selection of required bandwidthand arbitrary high operational frequencies.

BRIEF SUMMARY OF THE INVENTION

According to the embodiments presented herein, there is provided a3-degree of freedom (DOF) dynamic gyroscopic system comprising an outerframe, a central anchor, a detection mass coupled to the central anchor,a 1-DOF drive subsystem, a 2-DOF sense subsystem, and asymmetrically-decoupled suspension subsystem coupling the drivesubsystem to the outer frame and to the sense subsystem.

In one embodiment, the drive subsystem, sense subsystem andsymmetrically-decoupled suspension subsystem comprises two drive-modeshuttles coupled to the outer frame, two sense-mode shuttles coupled tothe outer frame, wherein each drive-mode and sense-mode shuttle isconstrained to translate only along its respective x or y axis, and aproof mass coupled to the two drive-mode shuttles, the two sense-modeshuttles, and the detection mass.

Another embodiment of the 3-DOF dynamic gyroscope system is where thetwo drive-mode shuttles and the two sense-mode shuttles are coupled tothe outer frame and to the proof mass via a plurality of uni-directionalsprings. The 3-DOF dynamic gyroscope system further comprises the proofmass being suspended in the x-y plane by the symmetrically-decoupledsuspension system, the proof mass being driven by the drive subsystemalong the x-axis to form a z-axis-rotation-sensitive element, and thedetection mass being constrained by the symmetrically-decoupledsuspension system to y-axis deflections.

In another embodiment, the 3-DOF gyroscope system the detection mass,proof mass form the coupled 2-DOF sense subsystem, wherein duringrotation of the proof mass, the proof mass generates a y-axis Coriolisforce, and wherein the y-axis constrained detection mass absorbs theCoriolis force from the proof mass and efficiently responds in a wideband formed by the two coupled resonant peaks.

In yet another embodiment, the symmetrically-decoupled suspensionsubsystem of the 3-DOF dynamic gyroscope system comprises means fordefining a sense-mode bandwidth by two resonant peaks and the frequencyregion in between in order to achieve optimal gain-bandwidthcharacteristics.

In yet another embodiment, the symmetrically-decoupled suspensionsubsystem of the 3-DOF dynamic gyroscope system subsystem comprisesmeans for optimally placing an operational frequency between thesense-mode bandwidth peak spacing of the gyroscope.

In yet another embodiment, the parameters of the detection mass, drivesubsystem, sense subsystem and symmetrically-decoupled suspensionsubsystem of the 3-DOF dynamic gyroscopic system comprise means forproviding increased gain and sensitivity depending on a predeterminedvalue of the mass ratio of the proof mass and the detection mass.

In yet another embodiment, each drive-mode shuttle and each sense-modeshuttle of the 3-DOF dynamic gyroscopic system further comprise aplurality of capacitive electrodes for the actuation, detection, andcontrol of the proof mass in the x and y directions.

In yet another embodiment, the detection mass of the 3-DOF dynamicgyroscope system further comprises a plurality of capacitors to detectthe oscillations induced by the Coriolis force of the proof mass.

In yet another embodiment, the 3-DOF dynamic gyroscope system furthercomprises means for the gyroscope to be adapted for use as an angularrate sensor for various applications such as camera stabilization,personal navigation, global positioning system augmentation, andelectronic stability control in automobiles.

According to another embodiment provided herein, there is provided amethod of operating a 3-DOF dynamic gyroscope system comprisingsuspending a proof mass in the x-y plane by a symmetrically-decoupledsuspension system, driving the proof mass along the x-axis to form az-axis rotation sensitive element by a drive subsystem, and constraininga detection mass to y-axis deflections by the symmetrically-decoupledsuspension system.

In another embodiment, the method further comprises rotating the proofmass, thus generating a y-axis Coriolis force, and absorbing theCoriolis force in the detection mass.

In yet another embodiment, where suspending a proof mass in the x-yplane by a symmetrically-decoupled suspension system of the methodcomprises defining a sense-mode bandwidth by two resonant peaks and thefrequency region in between in order to achieve optimal gain-bandwidthcharacteristics.

In yet another embodiment, wherein the symmetrically-decoupledsuspension system of the method further comprises optimally placing anoperational frequency between the sense-mode bandwidth resonant peaks.

In yet another embodiment, the method further comprises actuatingdetecting, and controlling the proof mass in the x and y directions viaa plurality of capacitive electrodes.

In yet another embodiment, the method of rotating the proof mass furthercomprises detecting the oscillations induced by the Coriolis force ofthe proof mass.

According to an embodiment presented herein, there is provided a methodof manufacturing a 3-DOF dynamic gyroscopic system which yieldsimplementations to a pre-selected operational frequency and sense-modepeak spacing comprising selecting two drive-mode shuttles, twosense-mode shuttles, a detection mass, and a proof mass, calculating therequired amount and location of a plurality of suspension elementsaccording to the pre-selected operational frequency and sense-modespacing, and coupling the suspension elements to the two drive-modeshuttles, the two sense-mode shuttles, the detection mass, and the proofmass.

In another embodiment of the method, the two drive-mode shuttles, thetwo sense-mode shuttles, the detection mass, and the proof mass areselected based on a desired die size and capacitance of the 3-DOFdynamic gyroscope system.

In a final embodiment, the method of manufacturing the 3-DOF dynamicgyroscope system comprises ensuring that the operational frequency isoptimally located between the sense-mode peaks even in the presence oflarge fabrication imperfections.

While the apparatus and method has or will be described for the sake ofgrammatical fluidity with functional explanations, it is to be expresslyunderstood that the claims, unless expressly formulated under 35 USC112, are not to be construed as necessarily limited in any way by theconstruction of “means” or “steps” limitations, but are to be accordedthe full scope of the meaning and equivalents of the definition providedby the claims under the judicial doctrine of equivalents, and in thecase where the claims are expressly formulated under 35 USC 112 are tobe accorded full statutory equivalents under 35 USC 112. The inventioncan be better visualized by turning now to the following drawingswherein like elements are referenced by like numerals.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view of the micromachined gyroscope with 1-DOF drivemode and a fully coupled 2-DOF sense-mode providing wide temperaturerobust bandwidth while minimizing the sacrifice in gain.

FIG. 2 a is a schematic diagram of the complete structure of thegyroscope.

FIG. 2 b is a diagram of the drive- and sense-mode lumped models, whilethe inset is a graphical representation of the response characteristicsof the gyroscope.

FIG. 3 a is a graphical representation of gain versus frequency for thesense-mode of the detection mass and the sense- and drive-modes for theproof mass of the gyroscope while the sense-mode frequency spacing iskept constant at 350 Hz.

FIG. 3 b is a graphical representation of gain versus frequency for thesense-mode of the detection mass and the sense- and drive-modes for theproof mass of the gyroscope while the operational frequency is keptconstant at 2.6 kHz.

FIG. 4 a is a graphical representation of the experimentalcharacterization of the gyroscope with lateral-comb drive electrodes inatmospheric pressure.

FIG. 4 b is a graphical representation of the experimentalcharacterization of the gyroscope with parallel-plate drive electrodes.

FIG. 5 a is a graphical representation of the characterization of thetemperature variations on the drive-mode of the gyroscope in air.

FIG. 5 b is a graphical representation of the characterization of thetemperature variations on the sense-mode of the gyroscope in air.

FIG. 6 is a graphical representation of the calibration rate plot,showing the measure relationship between angular rate input and thesensor voltage output.

FIG. 7 is a graphical representation of the response to the gyroscope toa fast dynamic angular rate excitation.

FIG. 8 is an example of two layouts of the micromachined gyroscope in across-shaped design, one with lateral-comb drive electrodes and anotherwith parallel-plate drive electrodes.

FIG. 9 is an example of two layouts of the micromachined gyroscope, thefirst in a crab-shaped design, and the second in a frame-shaped design.

FIG. 10 is a graphical representation of the effect of pressure on thesense-mode response of the gyroscope.

FIG. 11 is a graphical representation of the effect of temperaturevariations on a 1-DOF drive-mode of the gyroscope in a pressure of 75mTorr, including the frequency response, resonant frequency temperaturesensitivity, and Q factor sensitivity.

FIG. 12 is a graphical representation of the characterization of zerorate output noise modes, including the time history, ARW probabilitydistribution, Root Allan variance, raw output and Root Allan variance,filtered output.

FIG. 13 is a graphical representation of the characterization of zerorate output low frequency noise modes, including the time history andARRW probability distribution.

FIG. 14 is a graphical representation of the characterization of noisemodes at a constant nonzero rate of rotation, including the time historyand Root Allan variance.

The invention and its various embodiments can now be better understoodby turning to the following detailed description of the preferredembodiments which are presented as illustrated examples of the inventiondefined in the claims. It is expressly understood that the invention asdefined by the claims may be broader than the illustrated embodimentsdescribed below.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The current invention extends the design space of the previouslyreported gyroscopes with 2-DOF sense-modes and overcomes the limitationsimposed by the sense-mode DVA dynamics. The device, shown in FIG. 1, isnot just a minor optimization of previously reported designs, but rathera sharp conceptual deviation that introduces a new design architecturebased on a different arrangement of structural components favorablyshaping the response characteristics of robust gyroscopes.

The general structural diagram of the proposed gyroscope concept isshown in FIG. 2 a and is noted generally be reference numeral 10. Thestructure consists of an anchored outer frame 12, two drive-modeshuttles, 14, 16 two sense-mode shuttles 18, 20, a proof mass 22, adetection mass 24, and a central anchor 26. These structural elementsare coupled in a novel way to provide a 1-DOF drive- and 2-DOFsense-modes. The design space comprises five mechanical designparameters as described below.

The outer frame 12 is anchored to the substrate. The substrate (notshown) may be any material or material composite now known or laterdevised to those skilled in the relevant art. Each of the two drive-modeshuttles 14, 16 and each of the two sense-mode shuttles 18, 20 aresuspended relative to the outer frame 12 by two unidirectional springs,generally noted as reference numeral 28. The springs 28 restrict themotion of the shuttles 14, 16, 18, and 20 to their respective axes,which is the horizontal x axis of FIG. 2 a for the drive-mode shuttles14, 16 and the vertical y axis of FIG. 2 a for the sense-mode shuttles18, 20. Additional unidirectional springs 28 are used to couple the fourshuttles 14, 16, 18, and 20 to the proof mass 22. Alternatively, othersuspension means now known or later devised to those skilled in therelevant art may be used without departing from the spirit and scope ofthe invention. The described configuration of four shuttles 14, 16, 18,and 20, sixteen springs 28, which are identical and have an individualstiffness denoted by k₁/8, and the proof mass 22 forms a symmetricallydecoupled suspension. The current invention utilizes the conceptualarchitecture of the suspension as described above in a gyroscope with a2-DOF sense-mode for the first time.

The proof mass 22 can translate along both x (drive) and y (sense) axes.Using the electrodes on the drive-mode shuttles 14 and 16, the proofmass 22 is driven into a drive-mode oscillation to form a Corioliselement sensitive to rotation along the z-axis, which is perpendicularto the plane of FIG. 2 a. However, unlike previous devices found in theprior art, the Coriolis induced motion is not directly picked-up fromthe proof mass 22. Instead, the proof mass 22 is coupled to a second,detection mass 24, m_(d), by bidrectonal springs 29. The couplingsprings 29 are bi-directional, with equal x and y stiffnesses k₂. Thedetection mass 24 is also coupled to the substrate with an innerunidirectional suspension 28, k₃.

During rotation, the Coriolis acceleration of the proof mass 22 istransferred to the detection mass 24, which responds in a wide frequencybandwidth due to the coupled dynamics of the proposed 2-DOF sense-mode.Since the detection mass 24 deflection is constrained to the y directionsense-mode, the quadrature is minimized.

We denote the sum of the proof mass 22 and two drive-mode shuttles 14and 16 by m_(p) and the detection mass 24 by m_(d). The mass ratio isdefined as

$\mu^{2} = \frac{m_{d}}{m_{p}}$

and is generally less than one. FIG. 2 b shows the lumped element driveand sense dynamic model of the proposed gyroscope 10 (dampers are notshown for simplicity). The drive-mode is a single-DOF system with massm_(p) and stiffness k₁+k₂. The sense-mode is a complete 2-DOF system,with two masses, m_(p) and m_(d), and three stiffnesses k₂, k₃. Thedamping terms c₁, c₂, and c₃ are located parallel to the respectivespring elements 28. Even though the design includes multiple structuralelements, the x-y symmetry ensures that the proof mass'part of the 2-DOFsense-mode replicates the 1-DOF drive-mode, as shown symbolically by thedotted lines in FIG. 2 b.

The drive-mode dynamics is described by a second order transfer functiongiven below in equation 1:

$\begin{matrix}{{{{TF}_{p}(s)} = \frac{s}{{m_{p}s^{2}} + {\left( {c_{1} + c_{2}} \right)s} + \left( {k_{1} + k_{2}} \right)}},} & (1)\end{matrix}$

where the drive force is assumed to be the input to the system; velocityis taken as the output since it defines the amount of the Coriolis forceF_(c) generated by the proof mass 22. For the analysis, we assume thatthe drive-mode quality factor

${Q = {\frac{\sqrt{m_{p{({k_{1} + k_{2}})}}}}{c_{1} + c_{2}}10}},$

which is typical for bulk micromachined devices even at atmosphericpressure. Then, the drive-mode resonant frequency can be accuratelyapproximated by the undamped natural frequency given in equation 2:

ω_(n)=√{square root over ((k ₁ +k ₂)/m _(p))}.  (2)

The sense-mode dynamics can be described as a fourth order state-spacein terms of the proof mass 22 displacement x_(p) and velocity {dot over(x)}_(p), and the detection mass displacement x_(d) and velocity {dotover (x)}_(d). The equations of motion given in equation 3 are:

$\begin{matrix}{{\begin{bmatrix}x_{p} \\{\overset{.}{x}}_{p} \\x_{d} \\{\overset{.}{x}}_{d}\end{bmatrix}_{t}^{\prime} = {{\begin{bmatrix}0 & 1 & 0 & 0 \\\frac{k_{1} + k_{2}}{- m_{p}} & \frac{c_{1} + c_{2}}{- m_{p}} & \frac{k_{2}}{m_{p}} & \frac{c_{2}}{m_{p}} \\0 & 0 & 0 & 1 \\\frac{k_{2}}{m_{d}} & \frac{c_{2}}{m_{d}} & \frac{k_{1} + k_{2}}{- m_{d}} & \frac{c_{1} + c_{2}}{- m_{d}}\end{bmatrix}\begin{bmatrix}x_{p} \\{\overset{.}{x}}_{p} \\x_{d} \\{\overset{.}{x}}_{d}\end{bmatrix}} + \begin{bmatrix}0 \\u \\0 \\0\end{bmatrix}}},} & (3)\end{matrix}$

where the input signal u is the Coriolis acceleration experienced by theproof mass 22 in the sense direction, u∝(input angular rate)×(drive-modevelocity). The detection mass 24 does not move in the drive directionand thus does not produce a Coriolis force on its own.

If the y-axis displacement (or velocity) of the proof mass 22 isconsidered as an output of the system, the corresponding transferfunction has a zero (“anti-resonance” condition) at the frequency givenin equation 4:

ω₀=√{square root over ((k ₂ +k ₃)/m _(d))}.  (4)

The proof mass 22 anti-resonance frequency is always located between thetwo sense-mode resonances as seen in the inset of FIG. 2 b, and thusequation 4 provides a convenient design guideline for selectingparameters of the system.

Closed-form expressions for the two resonant frequencies of thedetection mass 24 are also needed for the correct design of the coupled2-DOF sense-mode. The selection of the resonant frequencies is governedby the eigenvalue equation:

ω⁴−ω²(ω_(a) ²+ω_(b) ²)+(ω_(a) ²ω_(b) ²−ω_(ab) ⁴)=0,  (5)

where

${\omega_{n}^{2} = \frac{k_{1} + k_{2}}{m_{p}}},{\omega_{b}^{2} = \frac{k_{1} + k_{2}}{m_{d}}},{{{and}\mspace{14mu} \omega_{ab}^{2}} = {\frac{k_{2}}{\sqrt{m_{p}m_{d}}}.}}$

These three frequencies are commonly used in 2-DOF systems design andhave intuitive interpretations: ω_(a) is the uncoupled natural frequencyof the proof mass m_(p), ω_(p) is the uncoupled natural frequency of thedetection mass 24 m_(d), and ω_(ab) is the coupling frequency. Solutionto the eigenvalue equation 5 is given by equation 6:

ω²=½[ω_(a) ²+ω_(b) ²±√{square root over ((ω_(a) ²−ω_(b) ²)²+4ω_(ab)⁴)}],  (6)

which defines the locations of the two coupled sense-mode resonances.

The available structural design parameters for the proposed gyroscope 10are the two masses m_(p) and 24 m_(d) and three stiffnesses k₁, k₂, andk₃. These five parameters define the location of the drive-mode resonantfrequency, i.e. the operational frequency of the gyroscope 10, and thelocations of the two sense-mode resonant peaks, which define thebandwidth of the gyroscope 10. In practice, the operational frequencyand bandwidth requirements are dictated by the specific application.Here, we derive closed form expressions for the five design parameters.During the design stage, these expressions can be evaluated to obtain agyroscope implementation with prescribed operational frequency andfrequency spacing.

We denote the desired operational frequency by Φ and the desiredsense-mode peak spacing by ΔΦ. In order to ensure the optimal nominalpositioning of the drive-mode resonance with respect to the 2-DOFsense-mode response, we require that the drive-mode resonance coincideswith the proof mass antiresonance in the sense-mode. This additionaldesign requirement means that ω_(n)=ω₀, or equivalently,

ω_(a)=ω_(b).  (7)

This relation completes the mathematical description of the designproblem, which can now be solved analytically. From equations 6 and 7,the two coupled resonant frequencies of the detection mass 24 are givenby equation 8:

$\begin{matrix}\left\{ \begin{matrix}{{\omega_{1} = \sqrt{\omega_{n}^{2} - \omega_{ab}^{2}}},} \\{\omega_{2} = {\sqrt{\omega_{n}^{2} + \omega_{ab}^{2}}.}}\end{matrix} \right. & (8)\end{matrix}$

We assume that the masses 22 and 24 of the gyroscope 10 together withthe capacitive electrodes are implemented first. Then, the threestiffnesses k₁, k₂, and k₃ become functions of the two masses 22 m_(p)and 24 m_(d), and selection of the desired operational frequency Φ andthe desired frequency spacing ΔΦ. Finally, the system of three algebraicequations defining the stiffnesses is:

$\begin{matrix}\left\{ \begin{matrix}{{{\Phi^{2} = \frac{k_{1} + k_{2}}{m_{p}}},{\Phi^{2} = \frac{k_{2} + k_{3}}{m_{d}}},}} \\{{{\Delta \; \Phi} = {\sqrt{\Phi^{2} + \sqrt{\frac{k_{2}^{2}}{m_{p}m_{d}}}} - {\sqrt{\Phi^{2} - \sqrt{\frac{k_{2}^{2}}{m_{p}m_{d}}}}.}}}}\end{matrix} \right. & (9)\end{matrix}$

Solving equation 9 for the stiffnesses yields equation 10:

$\begin{matrix}\left\{ \begin{matrix}{{{k_{1} = {{m_{p}\Phi^{2}} - k_{2}}},}} \\{{{k_{2} = {\Delta \; \Phi \sqrt{m_{p}m_{d}}\sqrt{\Phi^{2} - \frac{{\Delta\Phi}^{2}}{4}}}},}} \\{{k_{3} = {{m_{d}\Phi^{2}} - {k_{2}.}}}}\end{matrix} \right. & (10)\end{matrix}$

The unique solutions exist as long as Φ≧ΔΦ/2, which holds for anyphysically meaningful combination of the operational frequency and thefrequency spacing. In practice, the desired operational frequency isbetween 2 to 20 kHz, while the desired sense-mode bandwidth is in therange of a few hundred Hz. For these conditions, Φ²>>ΔΦ²/4, and a simpleyet accurate approximation for k₂ can be obtained as k₂≈√{square rootover (m_(p)m_(d))}ΔΦ.

Based on equation 9, a design algorithm is formulated that yields animplementation of the proposed gyroscope 10 with desired operationalfrequency and sense-mode peak spacing. In summary, the algorithm forselection of the structural parameters includes three steps. First, thedesired values for the operational frequency Φ and the sense-mode peakspacing ΔΦ are identified based on the application requirements. Second,the outer anchor frame, the four shuttles, the two masses m_(p), m_(d)and the inner anchor are designed in a form of mask layout according tothe desired die size, available microfabrication tolerances and desirednominal values of actuation and detection capacitances. Third, thenecessary stiffnesses k_(1,2,3) are obtained using equation 10, andimplemented in a form of mask layout. The procedure yields a designconcept implementation with the required operational frequency andsense-mode frequency spacing. Due to the high symmetry of the structure,the operational frequency is guaranteed to be optimally placed betweenthe sense mode peaks, even in presence of considerable fabricationimperfections as detailed further below.

Several different physical layout implementations of the currentgyroscope are presented. It is to be expressly understood that thedisclosed layout implementations are for purposes of illustration onlyand that other layout implementations currently in use or later devisedmay also be used without departing from the original spirit and scope ofthe invention. The main difference between the three layouts is in theimplementation of the 2D coupling flexure k₂, which consequently effectsthe layout of the detection mass 24 and Coriolis detection electrodes.FIG. 8 shows two versions of the first layout, designated as across-shaped layout. Two additional physical layouts, a crab-shapedlayout and a frame-shaped layout are shown in FIG. 9. Here, we deriveasymptotic expressions for the nominal gain of the proposed gyroscope 10and analyze how it is affected by the choice of the operationalfrequency and the sense-mode frequency spacing. In capacitivegyroscopes, velocity of the detection mass 24 is often directly measuredusing motional-current detection techniques. Thus, the gain of agyroscope's sense-mode can be defined without loss of generality as theamplitude of the detection mass 24 velocity normalized with respect tothe input Coriolis acceleration. A qualitative measure of thegyroscope's gain can be obtained by evaluating the gain of thesense-mode transfer function at the nominal operational frequency.Assuming the Coriolis acceleration is the input and velocity of thedetection mass 24 is the output, the gain of gyroscope 10 is defined as:

$\begin{matrix}{{G_{V} = {{\frac{\omega_{a}}{\omega_{ab}^{2}}\sqrt{\frac{m_{p}}{m_{d}}}} = {{\frac{\Phi}{{\Delta\Phi}\sqrt{\Phi^{2} - {\frac{1}{4}\Delta \; \Phi^{2}}}}\sqrt{\frac{m_{p}}{m_{d}}}} \approx \approx {\frac{1}{\Delta\Phi}\sqrt{\frac{m_{p}}{m_{d}}}}}}},\mspace{20mu} {{{for}\mspace{14mu} \Phi^{2}}{{\Delta\Phi}^{2}/4}},} & (11)\end{matrix}$

where the effect of the damping terms have been ignored to simplify thequalitative analysis. The velocity gain G_(V) does not depend on theoperational frequency; it is inversely proportional to the frequencyspacing ΔΦ and to the square root of the mass ratio, μ=√{square rootover (m_(d)/m_(p))}.

For both the proposed gyroscope 10 and the DVA-based design the gain isinversely proportional to the sense-mode peak spacing. In the DVA-baseddesign, the peak spacing cannot be adjusted freely without a sacrificein detection capacitance and/or enlargement of the die due to the massratio constraint. This limitation is eliminated in the current device,where the peaks can be positioned arbitrary close to each otherindependent of the operational frequency and the mass ratio.

Here, we present modeling that illustrates and verifies the developeddesign approach. From the analysis, we derive the effects of operationalfrequency scaling and peak spacing in presence of damping. Based on theparameters of the experimentally characterized devices, we set thevalues of the proof mass 22 and detection mass 24 to m_(p)=4.72e-7 kgand m_(d)=1.35e-7 kg, so that μ²=0.286. The values of dampingcoefficients were set to

${c_{1} = {{1e} - {4\frac{N - s}{m}}}},{c_{2} = {{5e} - {6\frac{N - s}{m}}}},{{{and}\mspace{14mu} c_{3}} = {{2c_{1}} = {{2e} - {4{\frac{N - s}{m}.}}}}}$

It is assumed that the device is operated in air, the drive-mode qualityfactor Q is approximately 75, the damping between the proof mass 22 andthe detection mass 24 is relatively small, and the damping between theCoriolis detection parallel-plates is dominant due to the large overlaparea and narrow gaps.

FIGS. 3 a and 3 b show a simulation of the effects of the operationalfrequency and the sense-mode frequency spacing on the frequency responsecharacteristics of the gyroscope. The frequency responses of the drive-and sense-modes are analyzed assuming the force is the input andvelocity is the output. In FIG. 3 a the operational frequency isiterated through 1.3, 2.6, 5.2, and 10.4 kHz, while the sense-modefrequency spacing is kept constant at 350 Hz. The modeled responses showthat the velocity gain does not depend on the operational frequency,which agrees with the qualitative study of the gain. In FIG. 3 b theoperational frequency is set to 2.6 kHz, while the sense-mode peakspacing is iterated through 175, 300, 700, and 1400 Hz. The presentedcurves show that as the peak spacing increases, the gain consequentlydrops.

The modeling results confirm that the design approach indeed yieldsimplementations with the prescribed operational frequency and thesense-mode frequency spacing is independent of the proof and detectionmass values. Assignment of the operational frequency and the peakspacing is not constrained by the mass ratio. Also, the operationalfrequency is automatically positioned optimally between the sense-modepeaks, eliminating the need for trimming and tuning of the drive-mode.In gyroscope designs found in the prior art with a 2-DOF sense-mode, thecorrect positioning of the drive mode is not guaranteed by thestructural design due to the difference in suspensions outside andinside of the decoupling frame.

The sense-mode of the current gyroscope 10 can be designed in twoalternative ways. The two peaks can be placed far apart relative totheir individual bandwidths. This configuration is functionallyidentical to the previously proposed 3-DOF gyroscope. It can providevery wide bandwidth at the cost of the drop in the response gain. In theprevious DVA based design, the high-gain peaks cannot be incorporatedinto the bandwidth in devices with practical size and operationalfrequency, resulting in a lower sensitivity.

Due to the flexibility of the extended design space of the currentgyroscope 10, the two peaks can be placed close together. In this case,the sense-mode response of the detection mass 24 has an increasedbandwidth, composed of the two coupled resonant peaks and the region inbetween, while the gain is comparable to the mode-matched case. For thisconfiguration, the sense-mode dynamics is similar to coupledmicro-mechanical filters and can be shaped to a desired profile. Thedescribed configuration is preferable for applications requiringoperational frequencies in 2-20 kHz range and a bandwidth on the orderof 100-350 Hz.

The fabrication of the prototypes was done using an in house wafer-leveltwo-mask SOI process. P-type SOI wafers with a 50 μm thick device layerand a 5 μm buried oxide layer were used. The first mask was used todefine metallization of bonding pads using a lift-off process. Thesecond mask defined the structural layout. After patterning photoresistwith the second mask, the wafers were subjected to a Deep Reactive IonEtching (DRIE) using a Surface Technology Systems (STS) tool. Thefabricated wafers were then cleaned and diced. Individual devices werethen released in a HF acid bath. The minimal capacitive featuredimension of the process was 5 μm and the minimal structural feature was8 μm. An SEM image of a fabricated device with lateral-comb driveelectrodes is shown in FIG. 1. The fabricated devices were packagedusing a ceramic DIP-24 package and wirebonded for experimentalcharacterization.

Experimental characterization of the lateral-comb device in atmosphericpressure is shown in FIG. 4 a. The measured drive-mode resonantfrequency was 2.58 kHz and was located in-between the 2-DOF sense-moderesonances at 2.47 and 2.73 kHz. The measured drive-mode quality factorwas Q=140. A 250 Hz 3 dB cut-off bandwidth was formed in the sense-modeby the two resonant peaks and the region in-between. In thisconfiguration, the designed peak spacing is slightly wider than theoptimal due to overestimation of the damping during the design stage. Incase of parallel-plate drive electrodes, the damping term associatedwith the proof mass 22 increases about two times, which yields a 400 Hz3 dB sense-mode bandwidth as seen in FIG. 4 b.

FIG. 10 shows one embodiment of the present invention which demonstratesthe experimental characterization of the effect of pressure on the 2-DOFsense-mode frequency response. It confirms that the proof mass 22response has a zero (“anti-resonance”) at decreased damping levels.Also, as the damping is decreased, the gain at the two individualsense-mode peaks is increasing; the valley gain also increases, but at amuch slower rate. As a result, the peaks escape the 3 dB gain-bandwidthregion around the operational frequency, resulting in significantnarrowing of the bandwidth. In order to achieve optimal gain-bandwidthcharacteristics, the peaks should be incorporated into the bandwidth.Luckily, the proposed gyroscope 10 allows for arbitrary sense-modespacing. Depending on the expected packaging pressure and consequentlydamping levels, the two peaks can be designed to be close enough tomerge into one increased bandwidth, as discussed above. FIG. 10 is meantto be for illustrative purposes only and it is to be expresslyunderstood that additional similar embodiments using differentfrequencies may be used without departing from the original spirit andscope of the invention.

Temperature robustness of the gyroscopes, defined as the low sensitivityof the bias and scale factor to temperature variations, is a criticalperformance parameter of gyroscopes targeted for real-world harshenvironment applications, such as for consumer electronics, automotive,and defense industries. The fabricated prototypes were experimentallycharacterized in variable temperature environment using a custom made,package-level heater equipped with a feedback control.

FIG. 5 a shows characterization of the temperature drifts of thesingle-DOF drive-mode in air. Increase of temperature from 25° C. to125° C. results in a 2.25 dB drop in gain and a −8 Hz shift of theresonant frequency. The linear fit of the resonant frequency and gainversus temperature estimated the frequency temperature sensitivity of−31 ppm/° C., and the gain sensitivity of −2404 ppm/° C., respectively.In reduced pressure, the quality factor temperature sensitivityincreases by orders of magnitude.

In one embodiment, the temperature drift of the single-DOF drive-mode in74 mTorr vacuum is characterized in FIG. 11. Increase of temperaturefrom 25° C. to 85° C. results in more than 7 dB drop in gain as seenFIG. 11( c), and a −2 Hz shift of the resonant frequency, as seen inFIG. 11( b). From the measured data, the resonant frequency temperaturesensitivity is estimated as −12 ppm/° C., and the quality factorsensitivity is estimated as −9333 ppm/° C. While the resonant frequencytemperature sensitivity in vacuum is less than in air, the qualityfactor temperature sensitivity increases almost 4 times in vacuum. FIG.11 is meant to be for illustrative purposes only and the technical andimplementation features disclosed therein are not meant to limit thecurrent invention is any way. Similar features such as varyingtemperatures and pressures may be used without departing from theoriginal spirit and scope of the invention.

Drive-mode temperature drifts are easily mitigated by closed loopoperation. However, the severe drop of gain in the sense-mode can bedetrimental to accuracy of conventional mode-matched gyroscopes, wherethe scale factor changes several times over the typical temperaturerange. In the current gyroscope 10, the sense-mode temperature drift ofthe sense-mode is minimized by using the 2-DOF structure. Thiseliminates the need for any active temperature compensation for a widerange of operational temperatures, such as from −55° C. to 125° C.required for automotive applications.

Sense-mode frequency-response of the detection mass was experimentallycharacterized at 4 different temperatures ranging from 25° C. to 125° C.The results are shown in FIG. 5 b and reveal that the proposed designpossesses inherent robustness to temperature variations. Increase oftemperature from 25° C. to 125° C. results in approximately 1 dB changeof the gain in a 300 Hz bandwidth. The temperature change in thesense-mode gain evaluated at the corresponding drive-mode resonancefrequency is approximately 0.3 dB over a 100° C. range. This yields thescale-factor temperature coefficient of 351 ppm/° C.—almost an 8 timesimprovement compared to the 1-DOF case of −2404 ppm/° C., measured usingthe drive-mode. The temperature coefficient of the sense-mode phase wasdetermined as 0.08°/° C. The phase temperature coefficient is usedtogether with quadrature to obtain the temperature coefficient of thebias of the gyroscope 10.

We cite here temperature performance data of some of the most successfulcommercial MEMS gyroscopes. The uncompensated thermal sensitivities ofhigher performance quartz TFGs units from Custom Sensors andTechnologies (formerly Systron Donner/BEI) is 300 ppm/° C.; AnalogDevices' automotive-grade polysilicon angular rate sensor ADXRS150specifies scale factor uncompensated thermal sensitivity of 1700 ppm/°C.; highly optimized single crystal silicon Draper's design with 5-15%mismatched modes used in Honeywell's navigation systems has a 250 ppm/°C. scale factor temperature coefficient. The current gyroscope's 10uncompensated scale factor temperature coefficient of approximately 350ppm/° C. was measured using a first generation, proof-of-concept device,and is already on par with state of the art commercial vibratorygyroscopes. The thermal robustness of the proposed gyroscope can beimproved even further by increasing the spacing between the sense-moderesonant peaks using the design equations 10.

The angular rate performance of the prototype was experimentallycharacterized using a computer controlled Ideal Aerosmith 1291 BR ratetable. The gyroscope 10 was driven into 5 μm peak-to-peak resonantmotion using a combination of a 30 V DC bias and a 3.5 Vrms AC drivingvoltage applied to the anchored drive-mode lateral comb electrode. AnElectro-Mechanical Amplitude Modulation (EAM) technique was used todetect the Coriolis-induced motion in the sense-mode. The AC carriervoltage with 3.5 Vrms amplitude at 20.5 kHz frequency was applied to themobile masses; the anchored sense-mode parallel-plate electrode wasconnected to the inverting input of an operational amplifier, configuredas a transimpedance amplifier.

FIG. 6 shows the calibration curve obtained by programming the ratetable to constant angular rate motion and observing the correspondingvoltage output of the gyroscope. The collected data points were fittedwith a line to reveal the sensitivity of 28 μV/°/s. As only a singlesided capacitor was used, the total sensitivity of the device is 56μV/°/s for the same operational conditions. A 62.5°/s rate equivalentquadrature was measured by observing the out-of-phase output of thegyroscope at zero rate. Using the simple non-differential detectionscheme, the measured resolution was 0.09°/s√{square root over (Hz)}. Asdescribed in the prior art, the resolution is expected to improve toapproximately 0.01°/s√{square root over (Hz)} using a completedifferential detection scheme. FIG. 7 demonstrates another embodimentthat shows the response of the gyroscope 10 to a dynamic rateexcitation. The response, updated at a 10 ms rate, accurately traces thechanging rate; the 45 ms delay is due to the output filter (24 dB/oct,10 ms time constant) of the electronics. FIG. 7 is meant to be forillustrative purposes only and that the technical and implementationspecific features such as updating the response at a different rate arenot meant to limit the current invention in any way. Similar featuresmay be used without departing from the original spirit and scope of theinvention.

Using the structural characterization results presented in the previoussection, the gyroscope's 10 scale factor temperature sensitivity wasestimated to be 351 ppm/° C. The bias temperature sensitivity iscalculated as (quadrature)×(phase temperaturesensitivity)=(62.5°/s)×(0.00139 1/° C.)=313°/h/° C. FIG. 6 shows therate response curves for −55° C. and 125° C. temperatures calculatedusing the bias and scale factor temperature coefficients. The estimatedmaximum temperature drift over the 180° C. range is less than 4.6%.

In summary, we have presented a novel gyroscope design concept, whichutilizes a 1-DOF drive-mode and a fully coupled 2-DOF sense-mode,comprising two masses 22 and 24 with three suspension elements 28 and29. In order to achieve optimal gain-bandwidth characteristics, thesense-mode bandwidth is defined by the two resonant peaks and thefrequency region in between. Due to the high symmetry of the structure,the operational frequency is guaranteed to be optimally placed betweenthe sense-mode peaks even in presence of considerable fabricationimperfections. The provided closed form design equations allow forstraightforward realization of the concept for arbitraryapplication-specific operational frequencies and bandwidths. The ratesensitivity and quadrature of the gyroscope 10 are similar to the bestreported performance numbers for MEMS gyroscopes operated in air. At thesame time, based on the estimated scale factor temperature coefficientof −350 ppm/° C., a ±90° C. change of operational temperature results inonly a ±3% change of the gyroscope's 10 scale factor.

FIGS. 12 and 13 show additional embodiments in which characterizationand analysis of the noise modes in the gyroscope's 10 Zero Rate Output(ZRO). From the Root Allan Variance plot, FIG. 12( c), the measuredAngle Random Walk (ARW) is 0.09°/s/√{square root over (Hz)}, biasinstability is 0.08°/s, and Angle Rate Random Walk (ARRW) is0.03°/s×√{square root over (Hz)}. FIG. 14 compares noise performance ofthe gyroscope 10 at zero rate and at a 50°/s constant rate rotation.During rotation, the ARW stayed at the same level, while the ARRW andthe bias drifts slightly improved, indicating good in-operation noiseperformance of the gyroscope.

The noise performance numbers of the proposed gyroscope 10 arecomparable to performance of gyroscopes found in the prior art operatedin air despite the crude, non-differential, shelf-top electronics setup.As previously investigated, the rate equivalent noise is expected todecrease at least an order of magnitude upon employment of a completedifferential detection scheme, yielding ARW on the order of tens of°/h/√{square root over (Hz)}, ARRW on the order of single °/h×√{squareroot over (Hz)}, and bias instability not more than few tens of °/h. Thetechnical and implementation specific features contained within FIGS. 12and 13 are meant for illustrative purposes only and are not meant to belimiting the current invention in anyway. Similar features may be usedwithout departing from the original spirit and scope of the invention.

Many alterations and modifications may be made by those having ordinaryskill in the art without departing from the spirit and scope of theinvention. Therefore, it must be understood that the illustratedembodiment has been set forth only for the purposes of example and thatit should not be taken as limiting the invention as defined by thefollowing invention and its various embodiments.

Therefore, it must be understood that the illustrated embodiment hasbeen set forth only for the purposes of example and that it should notbe taken as limiting the invention as defined by the following claims.For example, notwithstanding the fact that the elements of a claim areset forth below in a certain combination, it must be expresslyunderstood that the invention includes other combinations of fewer, moreor different elements, which are disclosed in above even when notinitially claimed in such combinations. A teaching that two elements arecombined in a claimed combination is further to be understood as alsoallowing for a claimed combination in which the two elements are notcombined with each other, but may be used alone or combined in othercombinations. The excision of any disclosed element of the invention isexplicitly contemplated as within the scope of the invention.

The words used in this specification to describe the invention and itsvarious embodiments are to be understood not only in the sense of theircommonly defined meanings, but to include by special definition in thisspecification structure, material or acts beyond the scope of thecommonly defined meanings. Thus if an element can be understood in thecontext of this specification as including more than one meaning, thenits use in a claim must be understood as being generic to all possiblemeanings supported by the specification and by the word itself.

The definitions of the words or elements of the following claims are,therefore, defined in this specification to include not only thecombination of elements which are literally set forth, but allequivalent structure, material or acts for performing substantially thesame function in substantially the same way to obtain substantially thesame result. In this sense it is therefore contemplated that anequivalent substitution of two or more elements may be made for any oneof the elements in the claims below or that a single element may besubstituted for two or more elements in a claim. Although elements maybe described above as acting in certain combinations and even initiallyclaimed as such, it is to be expressly understood that one or moreelements from a claimed combination can in some cases be excised fromthe combination and that the claimed combination may be directed to asubcombination or variation of a subcombination.

Insubstantial changes from the claimed subject matter as viewed by aperson with ordinary skill in the art, now known or later devised, areexpressly contemplated as being equivalently within the scope of theclaims. Therefore, obvious substitutions now or later known to one withordinary skill in the art are defined to be within the scope of thedefined elements.

The claims are thus to be understood to include what is specificallyillustrated and described above, what is conceptionally equivalent, whatcan be obviously substituted and also what essentially incorporates theessential idea of the invention.

We claim:
 1. A method of manufacturing a 3-DOF dynamic gyroscopic systemwhich yields implementations to a pre-selected operational frequency andsense-mode peak spacing comprising: selecting two drive-mode shuttles,two sense-mode shuttles, a detection mass, and a proof mass; calculatingthe required amount and location of a plurality of suspension elementsaccording to the pre-selected operational frequency and sense-modespacing; and coupling the suspension elements to the two drive-modeshuttles, the two sense-mode shuttles, the detection mass, and the proofmass.
 2. The method of claim 1 where the two drive-mode shuttles, thetwo sense-mode shuttles, the detection mass, and the proof mass areselected based on a desired die size and capacitance of the 3-DOFdynamic gyroscope system.
 3. The method of claim 1 further comprisingensuring that the operational frequency is optimally located between thesense-mode peaks even in the presence of large fabricationimperfections.